[QUE/QFT-03001] QFT-PROBLEM

Prove the following commutation relations for the infinitesimal generators of the Lorentz group \begin{eqnarray}\nonumber [P^\mu , P^\nu ] &=& 0\\\nonumber [M^{\mu\nu} , P^\sigma] &=& i(g^{\sigma\mu} P^\nu - g^{\sigma\nu} P^\mu )\\\nonumber [M^{\mu\nu} , M ^{\rho\sigma}] &=& i(M^{\mu\rho} g^{ \nu\sigma} + M^{\nu\sigma} g^{\mu\rho} - M^{\nu\rho} g^{\mu\sigma} - M^{\mu\sigma} g^{\nu\rho} ) \end{eqnarray} Our notation is the same as that of Gasiorowicz, {\it Elementary Particle Physics} John Wiley and Sons (1968)